Reality consists of 3 spatial dimensions with time adding a fourth dimension. But what reason could we possibly have for putting such limits on reality? Do higher dimensions have any reality apart from their construction within a mathematical framework?
Plato believed in the reality of higher dimensions, as his allegory of the cave demonstrated. Claude Bragdon considered the fourth dimension to be spatial. He believed our conception of time as the fourth dimension was mistaken. We experience time as a “fourth dimension” because of our lack of ability in sensing this dimension which is spatial. He used an analogy equivalent to Plato’s cave analogy. A flatlander would experience a cube travelling through its plane-wise world as beginning with a point, expanding to a polygon and finally contracting to a point before disappearing from sight. It is obvious to me that this flatlander inhabits a three dimensional world and is itself three dimensional, but can only perceive in two spatial dimensions. It perceives itself and its fellow flatlanders as a polygon which changes over time. It conceives of reality as consisting in two spatial dimensions and one time dimension.
Rudolf Steiner discusses the dimensions of space and beyond in a collection of lectures and discussions collated in the book, “The Fourth Dimension. Sacred Geometry, Alchemy, and Mathematics.”
Here he considers beings consisting of various dimensions. A being of two spatial dimensions would only be capable of perceiving one dimension, a being of three dimensions would only perceive two dimensions and so on. In this resect we are beings of four spatial dimensions but we only perceive three of them. Although each of these three dimensions are unique. They all differ experientially.
Regarding the contemplation of the fourth dimension, Steiner admired the work of Charles Howard Hinton who has been credited with coining the word “tesseract” as the name for the four dimensional equivalent to the cube. As a cube can be represented in two dimensions by the hexagon, so the tesseract can be represented in three dimensions by the rhombic dodecahedron.
In Steiner’s lectures linked to above, he introduces his audience to the mathematical treatment of the higher dimension with accompanying diagrams. He also highlights the differences between mathematical treatment and the reality of further dimensions. He does not view reality as consisting of a series of ever increasing spatial dimensions. The neutralization of polarity in one dimension gives rise to the adjacent dimension. For example when two planes cross there arises a line. The planes give rise to the line but the line has no two-dimensional component.
He considers us to be six-dimensional beings with the three physical dimensions being a reflection of three higher causal, creative dimensions. The plants we perceive are three dimensional images of four dimensional beings. In his “archetypal plant” Goethe caught a glimpse of the reality of plants as four-dimensional beings.
Time is a projection of the fourth dimension into the three spatial dimensions of the physical world. It is a feature of living beings that they change intrinsically over time. Sentient beings encompass five dimensions and self aware beings encompass six dimensions. Thinking is dimensionless.
Now when we try to understand the connection between mind and matter some people regard this as a problem of interaction between an immaterial mind and a material body. This becomes a problem for both materialists and idealists to grapple with. But if we look at this from the point of dimensions we can see a solution. We can take an example of a similar problem in two-dimensional reality. In this two-dimensional world we can imagine a ring with a smaller disc sitting outside it. How can the disc get inside the ring without somehow interfering with the structure of the ring? This would be impossible if reality was limited to two dimensions. But if the disc could be lifted into the third dimension and then moved into the ring, this would seem like a miracle to any being perceiving in just two dimensions. It would be as if the disc disappeared and then reappeared within the ring. It is the same with an act of willing a part of my body to move, i.e. mind affecting matter. The connection does not occur in our familiar three dimensional spatial world but in the higher dimensions in which my inner sentient life belongs. This activity impinges on the three-dimensional world but it is not restrained by it.
Good point. Thinking is a living process. In order to fix a thought in our minds we have to kill the living thinking. But death is a very natural part of life. We have to accept that many of our thoughts have become static and dead and to engage more with living, flexible thinking.
I believe that in the beginning was the Word, and from what I can tell you believe that in the beginning matter was spewed out of “the big bang” or something similar.
Confused minds. Abstractions being confused by abstractions.
The curve of a thrown stone can be represented geometrically or algebraically. Do you see any difference in the level of abstraction between these ways of representing?
If we teach children to count by adding beans it abstracts out the connection between the beans. But if we teach them to count by taking a stick and breaking off a piece we get two out of what was a unity. If when then break off an additional piece we arrive at three. This reality of threeness is not dependent on who broke the stick, it could have been a human, ape, beaver or falling rocks. Have I invented the concept of threeness? Three would still have been generated in each case. That is the reality.
Do colours and sounds exist in the world? Are colours the product of our sensory and neurophysiological mechanisms? Are colours purely subjective? Are colours a feature of an objective reality? Is there a reality which is beyond subjective/objective distinctions? What are your thoughts?
Perhaps they are all abstractions or they all have some place within reality depending on the context and how each of us thinks about these concepts.
To me becoming involves time while being suggests a dimension beyond time.
It isn’t clear what you are asking there. “Curve” already names an abstract idea.
My thoughts is that these are bad questions that we shouldn’t ask, because they are based on conceptual errors and empirical falsehoods.
In particular the subjective/objective distinction is a complete muddle and one that we are better off not using at all.
It might be a more useful question to ask, what are the metaphysical and epistemological relationships between our lived experience of a world described with sensory properties and our best empirical science?
Think of a projectile which is not self propelled but leaves some sort of visible trail as it travels through the air. You will see a parabola exactly like the geometrical figure of a parabola.
I believe you are a mathematician, right? In what way does the equation of a parabola resemble the form of a parabola?
I would answer that even uninformed naive questions are worth asking. Any student that is discouraged from asking questions is actually being discouraged from learning. By the nature of the questions asked any decent teacher will get a better understanding of their pupil’s shortcomings and progress. Even “bad” questions can be helpful here.
The subjective/objective distinction might be regarded as a poor subject of discussion for professional philosophers. But I believe it’s a perfect topic for places like this. The average person has a good grasp on what could be regarded as subjective and what is objective. They certainly know the distinction between actions occurring in the world in general and actions directed at them personally. I would say that through experience we can understand the difference between the reality of subject/object and subject/object as abstractions. Getting caught up in over philosophizing leads away from reality towards arguing in the realm of abstractions.
I’m not sure what to make of that. It seems to be an attempt to compare incomparables.
Perhaps I should clarify my point about “curve” being an abstract idea. We see a curve as something that contrasts with straight. But “straight” is really a geometric idea. We don’t see anything straight in nature.
The “average person” is terrible at philosophy, which is one of the reasons why teaching it is challenging. Plato’s dialogues are masterpieces of how bad average people are at reasoning carefully, even about subjects that they believe they understand perfectly well. So appealing to what “the average person” understands (or misunderstands) isn’t illuminating.
One cannot think or communicate without using abstract concepts. If one thinks that abstract concepts interfere with direct awareness of reality, then one had best pursue the path of radical silence taught by Zen Buddhism.
The distinction between what is subjective and what is objective is a piece of philosophical jargon, invented by philosophers in order to solve philosophical problems. It was first made by Descartes, who wanted to reconcile St. Augustine with mechanistic physics as a way of preserving Christian doctrines when the scientific revolution required rejecting St. Thomas Aquinas’s synthesis of Christianity and Aristotle. The distinction was further refined and improved upon by Descartes’s immediate successors, until Kant showed that no philosophical progress could be made unless that distinction was radically re-thought. That reconceptualization paved the way for German Idealism and later developments.
As a consequence of those later developments, but especially in the versions accomplished by Merleau-Ponty and by John Dewey, I don’t think the subject/object distinction neatly tracks anything in experience; on the contrary, I think it distorts our understanding of what experience is.
That’s why I think that serious conversation about the metaphysics of sensory qualities cannot be done well within the subject/object framework.
And do you think that the physical parabola traced by an object is incomparable to the figure of a parabola drawn on paper?
We neither see anything straight nor any ideal parabolas or other curves in nature. But I do agree that nature produces curves and spirals everywhere. Spirals result from the polar interactions of radial forces and surrounding peripheral forces.
All I’m saying is that algebra is more abstract than geometry when it comes to working with the shapes and figures of the experiential world. Anyone can use the Pythagorean formula to work out the lengths of the sides of tringles without having a mental picture of how the squares can be manipulated to give the answer. Geometry allows one to see the process in the mind’s eye.
What is drawn on paper is a representation. So you question amounts to: is path of an object incomparable to a representation of a parabola?
When we construct representations, we do so in accordance with social conventions. If we try to compare, then we are perhaps following the same social conventions.
Do you think measurement by (generally electronic) instrumentation applies here anywhere? Agreement between instruments doesn’t seem to fit the notion of intersubjective. Instruments can measure much of what we regard as sensory qualities. Do you think such measurements properly reflect the notion of “objective”, or do they just make the notion of subjective slipperier?
I think there are two extremes here. There are those who have very little love of learning in general. Their only interest in what is going to benefit them personally. Favourite sayings here are, “every man for himself”, and, “look after number one”. Then on the right of the bell curve are those who are very interested in understanding reality for its own sake as they see it and get very tied up in the convolutions of difficult philosophical problems. I see myself as fairly average, moving around somewhere on the right hand slope of the curve.
I would hope that those who are on the extreme left move away from the left as they get older and wiser, but it’s not guaranteed. Moving too far to the right brings the danger of adopting a narrow stance in which all other points of view are dismissed out of hand.
Of course abstract concepts feature heavily in any communication. There is nothing wrong with this as long as their rightful place is understood. Plato’s Forms are an abstraction from the perspective of physical reality as they are found nowhere in that domain. But physical reality is itself an abstraction from a higher standpoint.
It isn’t a matter of arguing within a subject/object framework, but of trying to understand where the divide is generally assumed to be and its consequence on human behaviour. In my opinion the evolution of consciousness there is a stage which involves a feeling of being a separate subject within an objective world. Only in this way can love for the “other” be developed. And when this love reaches a high degree, the subject/object dichotomy is overcome and an understanding of the higher unity of the whole of existence comes about.
The subject/object distinction is a necessity in the evolution of consciousness.
The path of an object, like the drawn curve, is also a representation of a parabolic curve. Individual curves vary, human conventions vary, human societies and cultures vary, but the concept of conic sections does not change because any of these change.
Subjectivity goes hand in hand with self consciousness. Mechanical devices have never shown any signs of self consciousness.
I’m not sure what point you think you are making there. It is quite possible for somebody to live a reasonably complete life while never even hearing of conic sections.
But the people who design them, use them and interpret their outputs certainly do. You don’t seem to grasp the nature of the problem here.
Yet many other philosophers, such as Marx and Nietzsche, have argued that the very idea of a higher standpoint is only an abstraction from physical reality. How do you know that Plato and Steiner are right, and that Marx and Nietzsche are wrong? What arguments convinced you?
I haven’t given nearly as much thought to measurement as I have to the nature of models, though I recognize that they are inseparable aspects of scientific practice.
I think that the fact that we can build transducers (mechanical, electric, and electronic) that respond to features of the world that we can also respond to is certainly quite interesting — as well as the fact that we can use instruments to augment our sensory range.
Of particular interest to me is our capacity to demonstrate through experiment that other animals can detect features of the environment that we cannot (e.g. seeing polarized light, sensing infrared or ultraviolet parts of the EM spectrum, sound frequencies below or above the normal human hearing range).
(A friend of mine told me the other day that California ground squirrels have evolved a threat evaluation display that contains an IR component, because rattlesnakes are IR responsive, even though the squirrels themselves aren’t. That’s the kind of thing that fascinates me!)
Here, in a small-ish nutshell, is how I generally see the nature of epistemological problems:
Humans, like every other animal, are generally pretty good at detecting, classifying, tracking, and responding to motivationally salient stimuli, especially those stimuli that are relevantly similar to perceptible features of the physical and social environments that shaped mammalian, hominoid, and hominid evolution.
But because what matters to the animal depends on the ecological niche and developmental pathway constraints, animals are generally bad at deploying their perceptual and conceptual resources in contexts that depart too widely from their epistemic ‘home turf’. And generally pretty good means, of course, satisficing, not optimal. (I find it more intuitive to think of natural selection as selection against non-satisficing traits rather than as selecting for anything, let alone optimality.)
So every animal, including us, occupies what could be called an “epistemic local optimum”: generally pretty good at deploying the perceptual and conceptual capacities for detecting, classifying, tracking, and responding to motivationally salient stimuli.
But we’re also ok-ish (not great) at finding ways of moving away from our evolved epistemic local optimum in search of better ones. There are two major tricks that we use to do this.
The first is a semantically and syntactically rich language allows us to encode, transmit, and decode representations that would otherwise be wholly brain-bound, so that each of us can incorporate into our cognitive model information that we otherwise wouldn’t be able to access. (The encoding and decoding are lossy, so we compensate for that in iteration, e.g. “I don’t quite follow what you mean. Could you put it another way?”)
This allows for a transition, along a continuum, from purely egocentric models of the environment to more allocentric models. The more allocentric information that enters into our cognitive model, the more that model will approximate the real underlying structure of the universe. But there are ethnogenic, anthropogenic and biogenic constraints that impose limits on how approximate our models can become — and learning more about those constraints gives us some resources for how to work around them, as best as we can.
The second trick is the extraction of resources from the environment that can be used to extract other resources from the environment, e.g. tool-use. What makes human tool-use distinct from tool-use in other apes is the planning depth necessary for crafting and using tools, which requires extensive training and teaching.
Amongst other apes, young will carefully observe what elders are doing and figure out for themselves how to produce the same effect, which they will refine through trial and error. But the elders very rarely (if ever) set upon the task of constructing a special kind of task environment for the young in which the young will be expected to observe and also imitate the behavior being modeled for them. By contrast, explicit teaching and imitative learning are found in every single human culture.
These two good tricks — language and tool-use — are brought together in science. (Arguably science adds a third trick, mathematics. But mathematics could be understood as a formal language.) In science we come up with ideas about how the world might be, decide which parts of the model are variables and which are parameters, and then figure out how to construct a manipulation of the environment that allows us to measure the variables while leaving the parameters alone.
What is crucial about science is that we can experiments can fail, we can be surprised, we can find out things that we weren’t expecting and didn’t even know to look for. This is what gives us any degree of assurance that scientific methods will allow us to peek over the limits of our epistemic local optimum and catch glimpses of how the world really is.
And of course the picture that I have sketched for us about the nature of our epistemic situation is a picture based on what science seems to tell us about ourselves; it is not a picture that would have been available to Plato, Confucius, Nagarjuna, or Kant.
At the same time, our philosophical confidence in this picture is bolstered by giving us answers to questions that Plato and Kant were utterly mystified by, and to which they could give no intellectually satisfying response. So in that regard I do think that there is philosophical progress, insofar as we can use our best explanations of the world (and ourselves as part of that world) to address the questions posed by the greatest (so far) of human minds.
Thank you for this — it makes so much sense. I found your comments on allocentric models and surprise in science particularly on point.
That is true. The ideal conic section does not depend on any individual ideation of conic sections. The ideal conic section is. In other words it not becoming, it is being. And that is why Plato laid such stress on thinking about geometry. It leads beyond becoming.
I was making an observation, I wasn’t arguing against what you said.
In discussing the evolution of consciousness in the historical period, Owen Barfield used three terms, original participation, idolatry, and final participation.
Original participation is the state in which people do not feel separate from surrounding nature, They were/are part of ensouled nature and experience no subject/object dichotomy. Modern materialistic thinking has brought with it idolatry when we experience ourselves as apart from the “things” existing in an outer world and these “things” are imagined to have a reality greater than they deserve. The rise to final participation brings a reconnection without the loss of our sense of self and a realization that consciousness is not restricted within organs such as brains or skin.
As in your example of instruments, they cannot exist outwith the context of human designers. In reality there are no separate “things”. The jigsaw of reality is a unified picture.
Forms such as the triangle in the ideal sense belong in a higher reality. They are abstract with respect to our physical world because they are found nowhere within this reality. But to think that the ideal triangle is abstracted from physical triangles is to think that the perfect and consistent is a copy of the imperfect and inconsistent.
This is what Barfield was getting at with his concept of idolatry. Physical triangles are transient and subject to the processes of becoming are seen to have a greater reality than the ideal triangle. This triangle is not subject to the processes of time and cannot be broken or destroyed as the physical representation can. They have no part in becoming.
Isaac Asimov wrote that the most important words in science are not “Eureka, I’ve found it!” but rather “hmm, that’s funny…”
Steiner had a very high opinion of Nietzsche as can be seen from his book Friedrich Nietzsche, Fighter for Freedom. He wrote:
Nietzsche’s sister had allowed Steiner access to Nietzsche towards the end of his life and he gave a Memorial Address after his death.
Regarding Marx, Steiner speaks about The Communist Manifesto
And today we are seeing first hand the consequences of a thinking which stirs up hatred between groups of people.
Steiner predicted this time in which we can opt for two paths, one in which life is seen as having no meaning and this type of thinking leads ultimately to a “war of all against all”. Or we can choose the other path which leads to unity. We can either turn the illusion of separateness into a reality or we can come to an understanding of the higher unity which takes inner effort and sacrifice to achieve.
The future is in no way guaranteed.
I don’t know that the former are right and the latter wrong. I only know what I know from my own experience and due to my experiences I am more inclined towards Plato and Steiner. But I don’t believe that everything they say is true.
I prefer to leave room for doubt rather than to believe anything with certainty.
It is rather obvious that your “room for doubt” is not distributed equally between the views that KN was contrasting.
Why are you … ah … more inclined towards Plato and Steiner? What arguments made you prefer their views?
Too bad you don’t understand Marx or Nietzsche well enough to realize that Steiner is lying to you about what they are saying.
I’m done here.
I think this would apply to any of us here.
The arguments I’ve been using throughout my time here.
Steiner’s method of gaining knowledge of the world lays great emphasis on the process requiring self improvement and self discipline to accompany any gains in knowledge. Similar to the Buddhist eightfold path it is designed to ensure that knowledge is used wisely for the benefit of all and that it isn’t used for self-gratification.
Take a look at the newsreel images flashing across our screens at the moment and you will see the application and advances of technical knowledge in comparison to the wisdom of humanity which lags so far behind our creative abilities.
His book, Knowledge of the Higher Worlds and Its Attainment lays out the path that is open for anyone who wishes to follow it.
That’s a pity.
Have you read Steiner’s book, Friedrich Nietzsche, Fighter for Freedom?
Or anything Steiner said about Marx and the clarity of his thinking which allowed it to be taken up by so many people?
Steiner on Marx:
No, I have not. The short excerpt you shared above was enough to convince me that reading Steiner on Nietzsche would be a waste of my time — and I say that as someone who has read all of Nietzsche and published on Nietzsche.
The few excerpts from Steiner about Marx make it perfectly clear that Steiner doesn’t understand Marx at all.
Marx does not deny the importance of human individuality and Marx does not base the solidarity of the proletariat upon their hatred of the bourgeoisie. These are not only false but obviously false to anyone who has taken any time to read Marx.
Either Steiner is lying when he claims to have read them, or he has read them and he is lying about what they say.
If you look to Steiner for an understanding what Nietzsche and Marx are saying, you are being duped.
Funny, I can’t think of a single example where Steiner’s method resulted in some useful “gain of knowledge”. I did note you posting an OP bemoaning how genuine scientific knowledge resulted in a “mechanical and mindless” universe bereft of meaning. You must be looking at a different universe 😀 .
― Terry Pratchett, A Hat Full of Sky
Steiner’s preface from 1895 to the book I linked to:
The consensus of Nietzsche scholars is that Salome was right — Paul Ree was a substantial influence on Nietzsche, as Nietzsche himself admits.
I don’t think we can discount the possibility that Steiner is attacking Salome because she and Elisabeth hated each other, and Steiner is taking Elisabeth’s side out of personal loyalty. I also don’t think we can discount the possibility that Steiner rejects the possibility of Ree’s influence on Nietzsche because Ree was Jewish.
Elisabeth Foerster-Nietzsche’s anti-semitism is extensively documented.
Can you read German proficiently? I don’t think you can accuse Steiner of lying based on that short, isolated quote.
Steiner was not talking about the thoughts of Marx on individuality. He was talking about the effects of taking up such a philosophy which encourages setting up opposition between groups while stifling individuality by creating a false idea of equality among people. Steiner’s idea of threefolding lays out a system where equality and individuality have their proper places. History, and the current world situation, shows us that trying to set up a system which aims to produce a blanket equality is doomed to failure and conflict. Equality is appropriate for the political and rights sphere, but not the cultural nor the economic spheres. Marxism lost its way because it was so tied up in the economic sphere.
Marx may not have intended to promote a system that produced hatred and strife between groups of people but that has been the outcome. Steiner saw that both one-sided communism and extreme fascism have the same disastrous consequences. Neither take heed of the natural threefoldedness of humans which should be mirrored in society. He warned that this misplaced form of communism “will eat its way further and further into the world”. And that is what happened.
Isn’t it the height of arrogance to claim to “know how it’s done”. I side with Socrates, relatively speaking, I know that I know nothing.
In Metamorphoses of the Soul – Paths of Experience Vol. 2 (1910) Steiner wrote:
He obviously did not reject Ree’s influence.
Steiner seems to have understood the relationship between Salome, Ree and Nietzsche. I don’t know enough about this to say much more than that, but it looks like it would be interesting to dig deeper into this. As far as I know Steiner regarded Elisabeth Foerster-Nietzsche’s understanding of her brother’s writings as pretty poor to say the least.
What a peculiar attitude. Is it the aim of “Steiner’s method of gaining knowledge of the world” to end up knowing nothing?
Don’t think that’s correct. Where has Marxism been attempted? Cuba?
I might have gained knowledge a million-fold throughout my life but it would still amount to virtually nothing compared to what I’ve still to learn. I would say that this is what Socrates was getting at.
Do you not think that Lenin and Stalin were Marxists?